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Steph_Rawr352 Group Title

*~*~*~*HELP PLEASE*~*~*~* Factor 400x^2 + 160x + 16 completely.

  • one year ago
  • one year ago

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  1. Steph_Rawr352 Group Title
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    Oh.. and I have to factor it using a special product or something?

    • one year ago
  2. Aylin Group Title
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    a=400, b=160, c=16 ac=6400 We need to find factors of 6400 that add up to 160 do start the problem.

    • one year ago
  3. Steph_Rawr352 Group Title
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    80 and 80

    • one year ago
  4. Aylin Group Title
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    Ok. Now we will form this square:\[\left[\begin{matrix}400x^{2} & 80x \\ 80x & 16\end{matrix}\right]\]Notice that ax^2 is the first element of the first row, c is the second element of the second row, and the two factors times x are the other two entries (it doesn't matter which spot you put the factors in). Now, the next step is to find the greatest common factors of each row and each column. For example, the row with 80x and 16 has 16 as its greatest common factor. (In your work write this in front of the that row. I would show you exactly what I mean, but I don't think the formatting here will let me do it.) Then do that with the rest of the rows and columns. Finally, take those factors that you found and they will be the factored solution. The factors for the columns will be one set of parenthesis, and the factors for the rows will be the other set.

    • one year ago
  5. rizwan_uet Group Title
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    400x^2 + 160x + 16 = (20x)^2 +160x+4^2 = (20x)^2 +2(20x)(4)+4^2 can you do it now??

    • one year ago
  6. rizwan_uet Group Title
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    hint: a^2+2ab+b^2 = (a+b)^2 = (a+b)(a+b)

    • one year ago
  7. Aylin Group Title
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    The only other thing to expand it to a more general case (where you would say have negative factors or a is negative) is that the factor you write in front of the row or above the column has the same sign as the closest element to it. So for example if a was negative, the factor for that row would be negative, regardless of whether or not the other entry in that row was negative or positive. The same holds true for that column.

    • one year ago
  8. Steph_Rawr352 Group Title
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    @Aylin I don't understand the square thing with the ax^2 and c? and @rizwan_uet where would you put the factors that add up to 160?

    • one year ago
  9. Aylin Group Title
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    That's just a box you put the entries into to help with factoring.

    • one year ago
  10. Steph_Rawr352 Group Title
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    oh ohk thanks

    • one year ago
  11. Aylin Group Title
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    When you have your final answer you can post it here and either I or rizwan should be able to tell you if it is correct or give some more help if needed.

    • one year ago
  12. Steph_Rawr352 Group Title
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    ohk i will(: Thanks guys I wish I could pick 2 best answers

    • one year ago
  13. Steph_Rawr352 Group Title
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    I got (20x + 4)^2

    • one year ago
  14. Aylin Group Title
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    That does work, but it is not the simplest form. 20x and 4 both share a factor of 4. Do you know how to make it simpler?

    • one year ago
  15. Steph_Rawr352 Group Title
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    so it would be 5x + 1?

    • one year ago
  16. Aylin Group Title
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    Sort of. \[(20x+4)^{2}=(4(5x+1))^{2}=16(5x+1)^{2}\]

    • one year ago
  17. Steph_Rawr352 Group Title
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    oh ohk thank you!!

    • one year ago
  18. rizwan_uet Group Title
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    you have this ok (20x)^2 +160x+4^2 now from the factors (20x)^2 and 4^2 i can write (20x)^2 +2(20x)(4)+4^2 because i know the formula a^2+2ab+b^2 = (a+b)^2 thus (20x)^2 +2(20x)(4)+4^2 = (20x+4)^2

    • one year ago
  19. rizwan_uet Group Title
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    now (20x+4)^2 = (20x+4)(20x+4) thus the required factors are (20x+4)(20x+4)

    • one year ago
  20. Steph_Rawr352 Group Title
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    oh I understand now thank you so much!

    • one year ago
  21. rizwan_uet Group Title
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    welcome

    • one year ago
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